Browsing by Subject "Differential invariants"

Now showing items 1-9 of 9

    • Article  

      Differential invariants for systems of linear hyperbolic equations 

      Tsaousi, Christina; Sophocleous, Christodoulos (2010)
      In this paper we consider a general class of systems of two linear hyperbolic equations. Motivated by the existence of the Laplace invariants for the single linear hyperbolic equation, we adopt the problem of finding ...
    • Article  

      Differential invariants for third-order evolution equations 

      Tsaousi, Christina; Tracinà, Rita; Sophocleous, Christodoulos (2015)
      We consider a general class of third order evolution equations. We construct differential invariants with the employment of the infinitesimal method that using equivalence groups. We use the differential invariants to ...
    • Doctoral Thesis  Open Access

      Differential invariants of hyperbolic equations 

      Tsaousi, Christina (Πανεπιστήμιο Κύπρου, Σχολή Θετικών και Εφαρμοσμένων Επιστημών / University of Cyprus, Faculty of Pure and Applied Sciences, 2009-03)
      Σε αυτή την διατριβή, πρώτα θα αναφερθούμε σε βασικούς ορισμούς των ομάδων μετασχηματισμών Lie, των απειροστών μετασχηματισμών και το αναλλοίωτο των μερικών διαφορικών εξισώσεων, τα οποία είναι χρήσιμα για τα επόμενα ...
    • Article  

      Differential invariants of the one-dimensional quasi-linear second-order evolution equation 

      Ibragimov, Nail Kh; Sophocleous, Christodoulos (2007)
      We consider evolution equations of the form ut = f(x, u, ux)uxx + g(x, u, ux) and ut = uxx + g(x, u, ux). In the spirit of the recent work of Ibragimov [Ibragimov NH. Laplace type invariants for parabolic equations. Nonlinear ...
    • Article  

      Invariants of two- and three-dimensional hyperbolic equations 

      Tsaousi, Christina; Sophocleous, Christodoulos; Tracinà, Rita (2009)
      We consider linear hyperbolic equations of the formut t = underover(∑, i = 1, n) uxi xi + underover(∑, i = 1, n) Xi (x1, ..., xn, t) uxi + T (x1, ..., xn, t) ut + U (x1, ..., xn, t) u . We derive equivalence transformations ...
    • Article  

      Laplace type invariants for variable coefficient mKdV equations 

      Tsaousi, Christina; Tracinà, Rita; Sophocleous, Christodoulos (2015)
      We consider a class of variable-coefficient mKdV equations. We derive the equivalence transformations in the infinitesimal form and we employ them to construct differential invariants of the respective equivalence algebra. ...
    • Article  

      Lie group analysis of two-dimensional variable-coefficient Burgers equation 

      Ivanova, Nataliya M.; Sophocleous, Christodoulos; Tracinà, Rita (2010)
      The modern group analysis of differential equations is used to study a class of two-dimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are ...
    • Article  

      On linearization of hyperbolic equations using differential invariants 

      Tsaousi, Christina; Sophocleous, Christodoulos (2008)
      In this paper we consider the general class of hyperbolic equations ux t = F (x, t, u, ux, ut). We use equivalence transformations to derive differential invariants for this class and for two subclasses. Then we employ ...
    • Article  

      On the invariants of two dimensional linear parabolic equations 

      Tsaousi, Christina; Sophocleous, Christodoulos; Tracinà, Rita (2012)
      We consider the most general two dimensional linear parabolic equations. Motivated by the recent work of Ibragimov et al. [1-3] we construct differential invariants, semi-invariants and invariant equations. These results ...